- New
-
Topics
- All Categories
- Metaphysics and Epistemology
- Value Theory
- Science, Logic, and Mathematics
- Science, Logic, and Mathematics
- Logic and Philosophy of Logic
- Philosophy of Biology
- Philosophy of Cognitive Science
- Philosophy of Computing and Information
- Philosophy of Mathematics
- Philosophy of Physical Science
- Philosophy of Social Science
- Philosophy of Probability
- General Philosophy of Science
- Philosophy of Science, Misc
- History of Western Philosophy
- Philosophical Traditions
- Philosophy, Misc
- Other Academic Areas
- Journals
- Submit material
- More
A Model‐Theoretic Property of Sharply Bounded Formulae, with some Applications
Mathematical Logic Quarterly 44 (2):205-215 (1998)
Abstract
We define a property of substructures of models of arithmetic, that of being length-initial, and show that sharply bounded formulae are absolute between a model and its length-initial submodels. We use this to prove independence results for some weak fragments of bounded arithmetic by constructing appropriate models as length-initial submodels of some given modelOther Versions
No versions found
My notes
Similar books and articles
An Independence Result on Weak Second Order Bounded Arithmetic.Satoru Kuroda - 2001 - Mathematical Logic Quarterly 47 (2):183-186.
A Remark on Independence Results for Sharply Bounded Arithmetic.Jan Johannsen - 1998 - Mathematical Logic Quarterly 44 (4):568-570.
Independence results for variants of sharply bounded induction.Leszek Aleksander Kołodziejczyk - 2011 - Annals of Pure and Applied Logic 162 (12):981-990.
The strength of sharply bounded induction.Emil Jeřábek - 2006 - Mathematical Logic Quarterly 52 (6):613-624.
On End‐Extensions of Models of ¬exp.Fernando Ferreira - 1996 - Mathematical Logic Quarterly 42 (1):1-18.
A note on sharply bounded arithmetic.Jan Johannsen - 1994 - Archive for Mathematical Logic 33 (2):159-165.
Models of Bounded Arithmetic Theories and Some Related Complexity Questions.Abolfazl Alam & Morteza Moniri - 2022 - Bulletin of the Section of Logic 51 (2):163-176.
A model-theoretic characterization of the weak pigeonhole principle.Neil Thapen - 2002 - Annals of Pure and Applied Logic 118 (1-2):175-195.
Preservation theorems for bounded formulas.Morteza Moniri - 2007 - Archive for Mathematical Logic 46 (1):9-14.
Analytics
Added to PP
2013-12-01
Downloads
26 (#850,497)
6 months
5 (#1,037,427)
2013-12-01
Downloads
26 (#850,497)
6 months
5 (#1,037,427)
Historical graph of downloads
Citations of this work
The strength of sharply bounded induction requires M S P.Sedki Boughattas & Leszek Aleksander Kołodziejczyk - 2010 - Annals of Pure and Applied Logic 161 (4):504-510.
Multifunction algebras and the provability of PH↓.Chris Pollett - 2000 - Annals of Pure and Applied Logic 104 (1-3):279-303.
The strength of sharply bounded induction.Emil Jeřábek - 2006 - Mathematical Logic Quarterly 52 (6):613-624.
Conservative fragments of $${{S}^{1}{2}}$$ and $${{R}^{1}{2}}$$. [REVIEW]Chris Pollett - 2011 - Archive for Mathematical Logic 50 (3):367-393.
References found in this work
Metamathematics of First-Order Arithmetic.Petr Hajék & Pavel Pudlák - 1994 - Studia Logica 53 (3):465-466.
PhilPapers logo by Andrea Andrews and Meghan Driscoll.
This site uses cookies and Google Analytics (see our terms & conditions for details regarding the privacy implications). Use of this site is subject to terms & conditions.
All rights reserved by The PhilPapers Foundation
Server: philpapers-web-559df78dcc-zvk2b uwo